Nonlinear structural behavior of a size-dependent MEMS gyroscope assuming a non-trivial shaped proof mass

In this paper, a size-dependent based non-classical mechanics model for the structural behavior of a MEMS (micro-electro-mechanical systems) gyroscope is investigated. The micro-cantilever based gyroscope is possessing a proof mass at its free end, assumed to hold a non-negligible length as compared to the micro-cantilever’s length. The proof mass is triggered through an actuating electrode and at the same time is assuming a sensing electrode together assuming parallel-plates capacitive arrangements. The governing equations of the micro-gyroscope system are derived within the framework of a modified couple stress non-classical mechanics theory. Based on the resulting equations, the static and dynamic analyses of the system are performed to estimate the pull-in instability voltages, natural frequency, and dynamic responses of the sensing electrodes near primary resonance that are caused by the use of point mass assumption and classical theory. A mixed based method involving both the Galerkin modal expansion procedure along with the method of multiple scales (MMS) technique is utilized to carry out the micro-gyroscope primary resonance analysis through plotting its respective frequency responses near its fundamental mode. Simulated results show that the proof mass dimension and its respective size effects play a substantial role in drastically changing the initiation of the system pull-in instability along its actuation direction, its fundamental natural frequency, and accordingly its dynamic amplitude along its corresponding sensing direction.